Infinite families of 2-designs from a class of cyclic codes
Infinite families of 2-designs from a class of cyclic codes
复制标题
来自一类循环码的 2-设计的无限族
DOI：
10.1002/jcd.21682
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发表时间：
2020
影响因子：
0.7
通讯作者：
Fan Cuiling
中科院分区：
文献类型：
--
作者：
Du Xiaoni;Wang Rong;Fan Cuiling
组合设计在编码理论、密码学、通信和统计学中有着广泛的应用。众所周知，代码中所有具有固定权重的码字的支持可能会给出一个‐设计。本文首先确定了一类由扩展循环码的对偶导出的线性码的权值分布。然后，我们获得了无限的2‐设计族，并从代码中具有固定权重的所有码字的支持中显式地计算了它们的参数。通过一个简单的计数论证，我们得到了指数级的2‐设计。
Combinatorial‐designs have wide applications in coding theory, cryptography, communications, and statistics. It is well known that the supports of all codewords with a fixed weight in a code may give a‐design. In this paper, we first determine the weight distributions of a class of linear codes derived from the dual of some extended cyclic codes. We then obtain infinite families of 2‐designs and explicitly compute their parameters from the supports of all the codewords with a fixed weight in the codes. By a simple counting argument, we obtain exponentially many 2‐designs.